Weighted Average Cost of Capital
And equivalent approaches
Review item
A
corporation is near bankruptcy. Why do the managers invest in bad risks?
Answer on bad risks
Managers
represent equity … at least they are supposed to. Risk gives them a chance to pull out of bankruptcy. Equity gets the gain. A bad outcome leaves them still bankrupt. Debt suffers the loss.
Capital Budgeting for the Levered Firm
Adjusted Flows
Present Value Average Cost of Capital
to Equity
Weighted
APV
Example
Adjusted-Present-Value (APV)
NPV
for an unlevered firm NPVF = net present value of financing APV = NPV + NPVF
Unlevered NPV
Unlevered
cash flows = CF from operations - Capital Spending - Added NWC - corporate taxes for unlevered firm. Discount rate: r0 PVUCF: PV of unlevered cash flows NPV = PVUCF - Initial investment
Net present value of financing side effects
PV
of Tax Subsidy to Debt Costs of Issuing New Securities The Costs of Financial Distress Subsidies to Debt Financing
Flow-to-Equity (FTE)
LCF
= UCF - (1 - TC) x rB x B PVLCF = Present value of LCF FTE = PVLCF - Portion of initial investment from equity Required return on levered equity (rS) rS = r0 + B/SL x (1 - TC) x (r0 - rB)
Weighted-Average-Cost-ofCapital
Discount
rate: rWACC PVUCF: PV of Unlevered Cash Flows Value = PVUCF - Initial investment for entire project
Summary: APV, FTE, and WACC
APV WACC FTE
Initial Investment Cash Flows Discount Rates PV of financing
All UCF r0 Yes
All UCF rWACC No
Equity Portion LCF rS No
Which is best? Use WACC and FTE when the debt ratio is constant Use APV when the level of debt is known.
Example p. 437: Project
Cash
inflows Cash costs Operating income Corporate tax Unlevered cash flow
Cost
500 360 140 47.6 92.4
of project
475
APV
Physical
asset of project is discounted
at .2. NPV = 92.4/.2 - 475 = 462 - 475 = -13 Borrowing 126.2295 (from B/S = 1/3) rB = .1 NPVF = TC x B = 42.918 APV = -13 + 42.918 = 29.918
APV recap
Value
= 475 + 29.918 = 504.918 Debt = - 126.2295 Equity = 378.6885 Debt/Equity = 1/3 Debt/(Debt + Equity) = 1/4
Flow to Equity
Cash
inflows 500 Cash costs - 360 Interest - 12.62295 Income after interest 127.37705 Corporate tax - 43.3082 Levered cash flow 84.06885
FTE (continued)
Cost
Borrowing
Cost
to equity
475 - 126.2295 348.7705
FTE: Required return on equity
rS
=r0 +(B/S)(1-TC)(r0-rB) B/S = 1/3 rS = .2 +(1/3)(.66)(.2-.1) = .222
FTE valuation
NPV
= - 348.7705 + 84.06885/.22… = 29.918 Same as in APV method. Now, same thing with WACC.
Find rWACC
rWACC
= (S/(S+B))rS+(B/(B+S))(1-TC)rB =(3/4)(.222) + (1/4)(.66)(.1) = .183
WACC method continued
NPV
= - 475 + 92.4/.183 = 29.918 All methods give the same thing.
Example: Start-up, all debt financed.
Cost
of project = 30 CF of project 10 before tax, 6.6 after. Discount rate for an all equity firm .2. NPV = 6.6/.2 - 30 = 3
More APV example
Tax
shield from borrowing 30 at rB=.1 = .1(30).34 = 1.02. Discounted value = NPVF = 10.2. APV = 3 + 10.2 = 13.2.
Leverage of the start-up
Not
100%. Value is 30 + 13.2. B = 30, S = 13.2 S/(B+S) = .305555555 (can’t expect a round number here)
Example continued. Do it again
Another
project, same as before. Retain debt-equity ratio. rWACC = (S/(B+S))rS + (B/(B+S))rB(1-TC) rWACC = .30555555rS +.694444 rB (.66) rS=r0 +(B/S)(1-TC)(r0-rB) rWACC= .15277777
Value, using rWACC
NPV
= -30 + 6.6/.1527777 =13.2 Lesson: WACC works when the debt equity ratio is established before the project and retained thereafter. APV works when the project changes the debt equity ratio
Cash flows to equity
Cost
to equity = 0 CF’s = (10-3)*.66 = 6.6-3*.66=.462 rS = r0 + (B/S)*(r0 –rB))(1- TC ) rS = .35 NPV = 4.62/.35 = 13.2
Review item
Complete
the following statement and explain briefly: nothing matters in finance except __________ and _________.
Answer: taxes and bankruptcy
Explanation.
Because of homemade leverage, capital structure doesn’t matter in the absence of taxes and bankruptcy. Taxes matter because debt generates tax shields. Bankruptcy matters because financial distress damages the assets of the firm.